The measured far-field patterns and the polarization characteristics of lasing beams are reported in Figs. REF (a-c), which agree with the simulated results shown in Figs. REF (d-i). The beam is mainly polarized in the vertical direction, agreeing with the selection rule of intersubband transitions [1]}. Despite the circular symmetry of the aperture, the far-field pattern is highly asymmetrical and is much broader in the vertical direction. As shown by Figs. REF (j,k) which illustrate the near-field patterns, the electric field inside the aperture is oriented similarly as the one of a subwavelength dipole antenna [2]}. As a result of the large diffraction angle, the vector Stratton-Chu model [3]}, [4]} must be applied for the far-field calculation and the scalar Kirchhoff theory [5]}, [6]}, [7]} is no longer valid. As a result, the beam divergence in the vertical direction is much larger than the one along the horizontal direction. The presence of the metallic aperture strongly enhances the relative intensity of the far field in the horizontal polarization created by the field discontinuity at the edges of the waveguide, as shown with more details in the Supplemental Material Sec. E.
